2. Let \(\mathfrak {H}\)  still be the abstract Hilbert space. Consider a fractional differential operator
in the Riemann-Liouvile sense (see [1]}) i.e. in the formal form, we have
\(\mathfrak {D}^{1/\alpha }_{-}f(t):=-\frac{1}{\Gamma (1-1/\alpha )}\frac{d}{d t}\int \limits _{0}^{\infty }f(t+x)x^{-1/\alpha }dx.\) 
